C.R. Bard Inc. agreed to settle a woman’s claims that one of its vaginal-mesh implants caused internal problems before a trial set for this month in New Jersey, two people familiar with the accord said. Bard officials agreed to pay an undisclosed sum to resolve Melanie Virgil’s claims that Bard’s Avaulta Plus insert caused urinary problems, said the people, who asked not to be named because they weren’t authorized to speak publicly about the settlement. Virgil’s case had been set for a Sept. 23 trial in state court in Atlantic City, according to court dockets.